﻿of 
  Atom* 
  and 
  Molecules. 
  863 
  

  

  A 
  first 
  rough 
  approximation 
  of 
  the 
  possible 
  configuration 
  

   of 
  such 
  a 
  ring 
  can 
  be 
  obtained 
  by 
  considering 
  simple 
  systems 
  

   consisting 
  o£ 
  a 
  single 
  ring 
  rotating 
  round 
  the 
  line 
  connecting 
  

   two 
  nuclei 
  of 
  minute 
  dimensions. 
  A 
  detailed 
  discussion, 
  

   however, 
  of 
  the 
  configuration 
  of 
  systems 
  containing 
  a 
  

   greater 
  number 
  of 
  electrons, 
  taking 
  the 
  effect 
  of 
  inner 
  rings 
  

   into 
  account, 
  involves 
  elaborate 
  numerical 
  calculations. 
  Apart 
  

   from 
  a 
  few 
  indications 
  given 
  in 
  § 
  5, 
  we 
  shall 
  in 
  this 
  paper 
  

   confine 
  ourselves 
  to 
  systems 
  containing 
  very 
  few 
  electrons. 
  

  

  § 
  3. 
  Systems 
  containing 
  few 
  Electrons. 
  The 
  Hydrogen 
  

  

  Molecule. 
  

  

  Among 
  the 
  systems 
  considered 
  in 
  § 
  2 
  and 
  found 
  to 
  be 
  

   stable 
  the 
  system 
  formed 
  of 
  a 
  ring 
  of 
  two 
  electrons 
  and 
  of 
  

   two 
  nuclei 
  of 
  charge 
  e 
  is 
  of 
  special 
  interest, 
  as 
  it, 
  according 
  

   to 
  the 
  theory, 
  may 
  be 
  expected 
  to 
  represent 
  a 
  neutral 
  

   hydrogen 
  molecule. 
  

  

  Denoting 
  the 
  radius 
  of 
  the 
  ring 
  by 
  a 
  and 
  the 
  distances 
  

   apart 
  of 
  the 
  nuclei 
  from 
  the 
  plane 
  of 
  the 
  ring 
  by 
  b, 
  we 
  get 
  

   from 
  (1), 
  putting 
  X 
  = 
  l 
  and 
  n 
  = 
  2> 
  

  

  h 
  1 
  

   o= 
  —jr,a 
  

  

  from 
  (I) 
  we 
  further 
  get 
  

  

  = 
  V3-1 
  =1 
  . 
  ( 
  

  

  F=- 
  v 
  " 
  =1-049. 
  

  

  From 
  (2) 
  and 
  (3) 
  we 
  get, 
  denoting 
  as 
  in 
  Part 
  II. 
  the 
  values 
  

   of 
  a. 
  co, 
  and 
  T\ 
  for 
  a 
  system 
  consisting 
  of 
  a 
  single 
  electron 
  

   rotating 
  round 
  a 
  nucleus 
  of 
  charge 
  e 
  (a 
  hydrogen 
  atom) 
  by 
  

   a 
  , 
  cd 
  , 
  and 
  \V 
  , 
  

  

  a=0-95<z 
  , 
  © 
  = 
  l'10«o, 
  TT 
  = 
  2-20vV 
  

  

  Since 
  TV>2TV 
  , 
  it 
  follows 
  that 
  two 
  hydrogen 
  atoms 
  

   combine 
  into 
  a 
  molecule 
  with 
  emission 
  of 
  energy. 
  Putting 
  

   W 
  =2-0. 
  10- 
  1L 
  erg(comp. 
  Part 
  1 
  1, 
  p. 
  488) 
  and 
  N= 
  6*2. 
  10 
  23 
  , 
  

  

  where 
  X 
  is 
  the 
  number 
  of 
  molecules 
  in 
  a 
  gram-molecule, 
  we 
  

   get 
  for 
  the 
  energy 
  emitted 
  during 
  the 
  formation 
  of 
  a 
  gram- 
  

   molecule 
  of 
  hydrogen 
  from 
  hydrogen 
  atoms 
  (W— 
  2\Y 
  )N 
  

   = 
  2*5 
  . 
  10 
  12 
  , 
  which 
  corresponds 
  to 
  6*0 
  . 
  10 
  4 
  cal. 
  This 
  value 
  

   is 
  of 
  the 
  right 
  order 
  of 
  magnitude 
  ; 
  it 
  is, 
  however, 
  con- 
  

   siderably 
  less 
  than 
  the 
  value 
  13 
  . 
  10 
  4 
  cal. 
  found 
  by 
  Langmuir 
  * 
  

   bv 
  measuring 
  the 
  heat 
  conduction 
  through 
  the 
  gas 
  from 
  an 
  

   incandescent 
  wire 
  in 
  hydrogen. 
  On 
  account 
  of 
  the 
  indirect 
  

  

  * 
  I. 
  Langmuir, 
  Journ. 
  Amer. 
  Chem. 
  Soc. 
  xxxiv. 
  p. 
  860 
  (1912). 
  

  

  